When Castle and Beckett arrive on the crime scene and Castle sees the body and exclaims, "Santa is dead?!," a quick shot is then shown of the "dead" body, which can be seen breathing.
Castle tells Beckett about the amazing 15-foot Christmas tree he has in his home. When they show the tree, it is clearly no more than about 9 feet tall. Nathan Fillion (Castle) is 6'1" and the tree is no more that 3 feet taller.
As part of the investigation, they look for heliports in Long Island City, NY. They say there are 5 but in fact there are no heliports in Long Island City.